Double Dividend with Involuntary Unemployment: <br />Efficiency and Intergenerational Equity

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Double Dividend with Involuntary Unemployment:

Efficiency and Intergenerational Equity

Mireille Chiroleu-Assouline, Mouez Fodha

To cite this version:

Mireille Chiroleu-Assouline, Mouez Fodha. Double Dividend with Involuntary Unemployment: Effi-ciency and Intergenerational Equity. Environmental and Resource Economics, Springer, 2005, 31 (4), pp.389-403. �10.1007/s10640-005-2040-7�. �halshs-00089913�

and Intergenerational Equity

Mireille Chiroleu-Assouline

EUREQua University Paris 1 PanthéonSorbonne and ERASME. EUREQua -University Paris 1 Panthéon-Sorbonne, Maison des Sciences Economiques, 106-112 Bd de l’Hôpital, 75647 PARIS Cedex 13. Tel : 33 1 44 07 82 24, Fax : 33 1 44 07 82 02. Email : assoulin@univ-paris1.fr

Mouez Fodha

University of Metz, and EUREQua - ERASME. ERASME - Ecole Centrale Paris, Grande Voie des Vignes, F 92295 Chatenay-Malabry Cedex. Tel : 33 1 41 13 14 51, Fax : 33 1 41 13 16 67. Email : fodham@cti.ecp.fr

April 27, 2004

Abstract. This paper analyzes the double dividend and distributional issues within an overlapping generations models framework with involuntary unemployment. We characterize the necessary conditions for the obtention of a double dividend when the revenue of the environmental tax is recycled by a variation of the labor tax rate. We show that an employment dividend may occur without any e¢ciency dividend and that the young generation is not always harmed by the …scal reform, even without any intergenerational transfers. Therefore, three dividends (environmental, e¢ciency and intergenerational equity) can simultaneously occur.

Keywords: Environmental tax, Intergenerational equity, Unemployment, Double dividend

JEL classi…cation: D60, D62, E62, H23, Q28

1. Introduction

This paper analyzes the double dividend and equity issues within an overlapping generations models framework with involuntary unemploy-ment. In the absence of altruism, the behavior of private agents ac-counts for an intergenerational environmental externality. The activity of present generations causes emissions of pollutants which deteriorate the environmental quality, harming the welfare of all future genera-tions. The solution which is usually advocated in order to internalize an environmental externality is the implementation of pigouvian taxes. One of the advantages of such an environmental tax is that it provides a public revenue, which can be recycled. This is the reason why it is often preferred to subsidies or emission quotas.

As governments use the revenues from pollution taxes to decrease other distortionary taxes, environmental taxes improve the quality of

environment and may also lead to an economic bene…t: this is the double dividend. These potential gains could be a powerful argument in favor of environmental taxation. The existing literature usually con-siders many kinds of second dividend: rise in employment, improved e¢ciency, improved distributional equity (the three kinds of dividend distinguished by Ekins (1995)) or rise in private pro…ts, cut in the cost of public funds, and so on. But Goulder (1995) emphasized that the only convenient criterion refers to economic e¢ciency, because any other economic bene…t is nothing else than a component of global welfare. Since his clari…cation paper, the double dividend has been un-ambiguously de…ned as the combination of an environmental dividend and an e¢ciency one (by achieving a less distortionary tax system). Nevertheless, an employment dividend can also be de…ned, which plays in favor of the e¢ciency dividend without coinciding with it. And moreover, beside these e¢ciency properties, it can be instructive to also investigate equity issues: when the distributional equity is im-proved by the recycling of environmental tax revenues, one could as well call this additional bene…t a third dividend. The objective of this paper is then to study the existence conditions of a double dividend (according to Goulder’s de…nition), but also the role of the employment dividend and the distributional equity issue. The distributional concern can be viewed between di¤erent classes of households (employed and unemployed, poor and rich) or between di¤erent generations.

In particular, environmental decisions have an impact on the welfare of both current and future generations, since environmental quality is a public good that di¤erent generations share. These intergenerational issues on environmental externalities or on taxation have already been widely studied in the economic literature but the overlapping gen-eration approach, suggested by Solow (1974), (1986), began only to be used for analyzing …scal problems concerning polluting goods by John and Pecchenino (1994), (1997), John et alii (1995), Howarth and Norgaard (1995), Fisher and van Marrewijk (1998). The main result of all these studies is that environmental taxation implies such a welfare loss for the older generations experiencing the …scal reform that its implementation can not be wished because the generation which would decide it would also bear the heaviest burden. This result originates in the fact that balanced environmental …scal reforms have generally not been considered.

The present paper integrates both the e¢ciency and intergenera-tional distribuintergenera-tional aspects of environmental taxes. By using an over-lapping generations model, under the assumption of involuntary un-employment, we examine whether a revenue-neutral increase in the

pollution tax compensated by a change of the labor tax can yield a double dividend. This general framework can be related to those of Bovenberg and Heijdra (1998), Chiroleu-Assouline and Fodha (2002) and Bovenberg and van der Ploeg (1996) but di¤ers from them in several ways. Bovenberg and Heijdra (1998) do not explicitly address the double dividend issue but investigate whether a higher pollution tax can be Pareto welfare improving by bene…ting all generations. In their paper, pollution is due to capital utilization while we assume that the …scal base of the environmental tax is consumption (which causes pol-lution) rather than capital; their paper focus mainly on optimal capital taxation which allows them to pay little attention to the employment issue.

The introduction of involuntary unemployment is the main di¤erence between the present paper and Chiroleu-Assouline and Fodha (2002) who show that, even in full-employment, an e¢ciency dividend is likely to occur, by contrast with the …rst studies on this issue (Bovenberg and de Moiij 1994). This result depends heavily on the capital in-tensity of the initial steady state equilibrium relative to the golden rule and on the value of the intertemporal substitution elasticity. But we will show here that the existence of unemployment adds another way for obtaining a double dividend. When the intertemporal substi-tution elasticity is equal or greater than unity, Chiroleu-Assouline and Fodha (2002) established that no double dividend could occur under full employment assumption, while we will show that such a double dividend can appear when there is initially involuntary unemployment. Moreover their paper addressed an optimality issue while the present one explicitly focuses on second-rank concerns. Lastly, we assume that involuntary unemployment is caused by an exogenous minimum wage rate, like Bovenberg and van der Ploeg (1996) (who do not consider more than one generation). But this is almost the only common point between their work and ours, since they essentially focus on optimal taxation issues and study a very peculiar concept of double dividend which does not correspond to Goulder’s de…nition.

In the second section, we present our model, which relies on stan-dard assumptions of the overlapping generations framework (Diamond 1965). This economy consists of two periods lived individuals working and consuming when young and consuming and being a¤ected by the quality of the environment only when being old. The government is …nancing its spending (public investment and unemployment bene…ts) with a labor tax and a pollution tax. We characterize, in the third section, the speci…cation of the …scal reform when the revenue of the pollution tax is recycled by a variation of the rate of social

contri-butions instead of by lump-sum transfer. The fourth section focuses on the necessary conditions for the obtention of a double dividend. We show …nally that, under some conditions about the variations of the unemployment rate and of the interest rate, an inter-generations distributional dividend can also be obtained.

2. The model

By assumption, population size remains constant: N individuals are born in each period t. Each individual supplies one unit of labor when she is young and earns a …xed real wage ¹wt if she works or a …xed

unemployment bene…t bt if she is unemployed. Let E (-t) be the

ex-pected life-cycle income and ut the probability1to be unemployed at

time t. She divides her income between …rst-period consumption cy_t and saving st; in the second period the individual consumes her saving

and the interest she earns. The welfare of an individual born at t is measured with the intertemporal utility function:

U ¡cy_t; co_t+1; ¦t+1¢= (1¡ ¯) ln cyt+ ¯

¡

ln co_{t+1¡ ° ln ¦}t+1¢

with co

t+1 denoting her consumption when old and ¦t+1 the level of

pollution at t + 1. The intertemporal discount rate is ¯=(1 ¡ ¯) (with 0 < ¯ < 1) and ° is the weight of the pollution externality in the welfare evaluation (° > 0).

The assumption that pollution only a¤ects the older’ welfare is the extreme case of any situation in which the older would be assumed to be more sensitive than the younger to the degradation of the envi-ronmental quality2_{(because of their wealth state but also because the}

satisfaction supplied by their leisure depends upon the environmental quality).

The real interest rate is rt+1. The pollution tax rate is ¿et (the pollution

is assumed to be due to consumption, with a the emission rate of pollu-tants - see below). For each period, the household’s budget constraints can be written as follows:

½

E (-t) = ¹wt(1¡ ut) + utbt= (1 + a ¿et) cyt + st

(1 + a ¿e

t+1) cot+1= (1 + rt+1) st (1)

The intertemporal budget constraint of the agent born at t is given by: py_t cy_t + po_t+1 c_t+1o = ¹wt (1¡ ut) + utbt (2)

where py

t = (1 + a ¿et) is the consumption price of the …rst period and

The household’s problem is to choose her consumption path to maxi-mize her lifetime utility subject to the intertemporal budget constraint. The …rst order conditions yield:

@U (:) @cyt @U (:) @co t+1 = 1¡ ¯ ¯ cot+1 cy_t = py_t po t+1 = (1 + a ¿ e t)(1 + rt+1) (1 + a ¿e t+1) (3)

This relation determines the optimal consumption and saving path of the representative household3_:

8 > > < > > : cyt = cy(ut; ¿et) = (1¡ ¯)E(-_pyt) t co_t+1= co¡ut; rt+1; ¿e_t+1¢= ¯E(-_po t) t+1 st= s (ut) = ¯E (-t) (4)

Production is described by the usual assumptions: the production sector consists of one competitive representative …rm, being character-ized by a production function which has constant returns to scale and satis…es the Inada conditions; assume that production function has a Cobb-Douglas speci…cation F (Kt;Lt) = Kt®L1t¡® where Kt stands for

capital and Lt for utilized labor. When ¹wt is …xed at a too high level

for the labor market to be cleared, there is unemployment: with our assumptions of identical households and exogenous labor supply, the unemployment rate equals ut and Lt = (1¡ ut)N . Output per capita

yt= Y_Nt is a function of capital per capita (kt = K_Nt), i.e. yt= f (kt) =

(1_{¡ u}t)

h

kt

1_¡ut

i®

: The maximization problem of the representative …rm is:

Max

kt

[f (kt)¡ ¹wt (1 + ¿wt) (1¡ ut)¡ (rt+ ±) kt]

with ¿w

t the rate of labor tax, wt the …xed real wage per unit of labor

and ± the depreciation rate of capital.

Since capital market is competitive, capital earns its marginal product: rt= r (kt; ut) = f0(kt)¡ ± = ® · _k t 1_{¡ u}t ¸®¡1 ¡ ± (5)

As far as labor is concerned, the marginal product will adjust to meet the …xed real wage:

(1 + ¿wt) ¹wt= f (kt)¡ kt f 0_(kt) (1_{¡ u}t) = (1¡ ®) · _k t 1_{¡ u}t ¸® (6)

Note that …xing the real wage leads to an exogenous real interest rate4_: rt = ® · (1 + ¿wt) (1_{¡ ®)} w¹t ¸®¡1 ® ¡ ±

We assume that government spending is entirely …nanced by current taxes. The government’s budget constraint is that its purchases (gt

per capita) must equal, at each period t; its tax revenues minus the unemployment bene…ts. The equilibrium of the government’s budget is:

a ¿e_t(cy_t + co_t) + (1_{¡ u}t) ¿wt w¹t¡ utbt= gt (7)

The pollution ‡ow is assumed to be due to the household’s con-sumption (waste production, for example), but the household’s welfare is a¤ected by the stock of pollution ¦t+1 during the second-period of

her life, whose dynamics is described by the following equation: ¦t+1= (1¡ h) ¦t+ a N ¡cyt+1+ cot+1

¢

(8) where h is the constant rate of natural absorption of pollution (h 2 [0; 1[) and a the emission rate of pollutants.

The equilibrium of the output good market can be written as follows: yt= cyt + cot+ kt+1¡ (1 ¡ ±) kt+ gt (9)

which yields, by substituting the zero-pro…t condition, the governmen-t’s budget constraint (7) and the household’s budget constraints (1), the following equation:

kt+1 = st (10)

which is similar to the equilibrium condition of the capital market (N st = Kt+1), meaning that the capital stock in period t + 1 is the

amount saved by young individuals in period t.

Equation (6) is one equation in the two unknowns, ktand ut, which

we can write as ut(kt), and substitute together with (5) into the optimal

consumptions and saving of household: this yields their values at the decentralized equilibrium. The dynamics of the economy is obtained by using the equilibrium of the capital market (10):

This equation implicitly presents kt+1 as a function of kt: The steady

state equilibrium is de…ned by kt+1 = kt= k¤, with k¤satisfying the

following equation of k :

k = s (u (k)) this leads to:

k¤= ¯ [ ¹w (1_{¡ u}¤) + bu¤] (11) which, together with equation (6) at steady state, determines the un-employment rate u¤_:

The steady state per capita capital stock is independent of the envi-ronmental tax rate ¿e_:

¯ ¯ ¯ ¯ ¯ ¯ k¤= _{1+A¯ (b}¯b_{¡ ¹w)} u¤_{= 1¡ Ak}¤₌ 1_{¡A¯ ¹}w 1+A¯ (b_{¡ ¹}w) (12) where5_: A = A ( ¹w; ¿w) = · ₁ ¡ ® (1 + ¿w_{) ¹w} ¸1 ® > 0

At the steady state equilibrium, the stock of pollution is given by: ¦¤= a

hfc

y_{¤(u; ¿}e_{) + c}o_{¤(u; r; ¿}e₎

g (13)

The unemployment rate is strictly positive (u¤_{> 0) if and only if}

the …xed real wage ¹w is greater than the full-employment equilibrium real wage wf e_{. Adding that the employment has to be non-negative}

(u¤_{< 1), one can obtain the following necessary and su¢cient existence}

condition for the steady-state equilibrium:

µ_{1 + ¿}w 1_{¡ ®} ¶ ® 1¡® > w¹ wf e > 1 with w f e_{= ¯1¡®}® µ 1¡ ® 1 + ¿w ¶ 1 1¡®

3. The speci…cation of the …scal reform

We assume an exogenous increase of the pollution tax rate, imposed by the government in order to control pollution. The amount of govern-ment’s purchases gt is assumed ex post invariant. This increase d¿e of

the pollution tax rate causes a variation of the labor tax rate d¿w_{. At}

the steady state equilibrium, the government’s budget constraint (7) can be written as follows:

The link between d¿e _{and d¿}w _{is obtained through the di¤erentiation}

of this constraint (with dg = db = 0)6. We will give some details about this di¤erentiation in order to clearly distinguish the di¤erent e¤ects of the …scal reform:

- e¤ect on the labor tax revenue:

d ((1_{¡ u}¤) ¿w w) = ¹¹ wh1_{¡ u}¤³1 + Eu=¿w

´i

d¿w

where Eu=¿w > 0 is the elasticity of the unemployment rate to

the labor tax rate. There are here two opposite e¤ects. An in-crease of the labor tax rate exerts a direct e¤ect on revenue, real wage remaining unchanged. The second e¤ect is an indirect one: as a consequence of the increase of the labor tax rate, the steady state capital stock decreases (E_k=¿w < 0), hence the

un-employment increases and its earnings reduces. The labor tax revenue is thus positively a¤ected (this is the La¤er-e¢ciency con-dition7_{) if and only if the rate e¤ect is greater than the base e¤ect}

(u¤_{(1 + Eu=¿}w) < 1).

- e¤ect on unemployment global expenses: b du

d¿w > 0

The rise in the labor tax rate increases the total labor cost and thus reduces the labor demand. Therefore the unemployment rate increases and the government’s expenses grow.

- e¤ect on the pollution tax revenue paid by the younger individuals: d (a ¿e cy) =³a cy¤+ a ¿e @c_@¿ye

´

d¿e+ a ¿e @c_@uy _@¿@uw d¿w

Here di¤erent e¤ects are also combined. When consumption re-mains unchanged, increasing the tax rate raises the tax revenue, but the …scal reform modi…es the …scal base: the direct e¤ect on the consumption price decreases the …rst-period consumption (@cy

@¿e < 0) while the indirect e¤ect through the labor tax increases

it when the labor tax decreases (@cy

@u ¡ @u @¿w + < 0).

- e¤ect on the pollution tax revenue paid by the older individuals: d (a ¿e co) =³a co¤+ a ¿e @c_@¿oe ´ d¿e+ a ¿e ³@c_@uo _@¿@uw +@c o @r @r @¿w ´ d¿w Concerning the consumption of the older individuals, the modi…ca-tion of the …scal base is obtained through the combinamodi…ca-tion of three

e¤ects: the direct e¤ect on the consumption price decreases the second-period consumption (@co

@¿e < 0), the indirect e¤ect through

the unemployment rate is the same as the previous one for the younger individuals (@co

@u < 0 and @¿@uw > 0) and the indirect e¤ect

through the interest rate (@r

@¿w < 0 and @c o

@r > 0) magni…es this

e¤ect.

The balanced …scal reform must then respect the following link between the variations of the pollution tax and of the labor tax:

d¿w= ¤ d¿e with, ¤ =_¡a [N ] |{z} (?0) [D1] |{z } (?0) + [D2] |{z} (<0) + [D3] |{z} (<0) (14)

Let us investigate the sign of ¤ (noting Ex=z the elasticity of x to

z): - [N] = cy_¤ Ã 1+ Ecy_=¿e < 0 ! + co¤ Ã 1+ Eco_=¿e < 0 !

is the e¤ect of the change in environmental tax on its revenue. There are both a value e¤ect (the tax revenue increases with the tax rate, for unchanged consumption) and a …scal base e¤ect (consumption decreases as the tax rate increases, thus the …scal base erodes) which work in opposite ways. - [D1] = ¹w " 1_{¡ u}¤ Ã 1+ Eu=¿w > 0 !#

is the e¤ect of the change of ¿w

on its …scal revenue. There are again both a value e¤ect (the …scal revenue increases with the tax rate, for unchanged wage) and a …scal base e¤ect (the unemployment rate increases as the tax rate increases, thus the …scal base erodes).

- [D2] =¡_¿bwu¤Eu=¿w

> 0

is the e¤ect of the change of ¿w_{(via the total}

e¤ects on unemployment) on revenues of the unemployed. There is only a …scal base e¤ect : [D2] < 0 (since b is unchanged).

- [D3] = a ¿ e ¿w à cy¤ Ecy_=u < 0 Eu=¿w >0 + co¤ " Eco_=u < 0 Eu=¿w >0 + Eco_=r > 0 Er=¿w < 0 #!

is the e¤ect of the change of ¿w _{(via the total e¤ects on the}

unem-ployment rate) on the …scal revenues of the pollution tax levied. When the labor tax rate rises, unemployment increases and thus the consumptions and the …scal revenues decrease. There is only a value e¤ect: [D3] < 0.

The sign of ¤ is ambiguous: it might have been expected that a cut in labor tax would be in any case allowed by an increase in the pollution tax rate, but it is not the case here, because the budget is assumed to be balanced ex post (during each period). Note that, when the labor tax is La¤er-e¢cient (and thus [D1] is positive), the sign of

the denominator is undetermined. So, even when both taxes are La¤er-e¢cient, the sign of ¤ is ambiguous. These results can be summarized as follows (¤ = ¡aN

D):

As an illustrative example, we have explicitly calculated ¤ in our very simple model, under some simplifying assumptions (± = 1). In that case, we show that the environmental tax is always La¤er-e¢cient but that the labor tax is La¤er-e¢cient only if the tax rate is small enough: ¿w_< ®b

(1_¡u¤)( ¹w_{¡b)+b(1¡®)}: Therefore, even in the simplest case,

the sign of ¤ depends on the parameters of the economy and on the initial labor tax rate.

4. The welfare e¤ects of the …scal reform

One can measure the welfare e¤ects of small …scal changes by the marginal excess burden. This marginal excess burden corresponds to the additional income that has to be provided to the representative household to keep her utility at its initial level (this is the compensatory income variation, denoted dRc): it stands for the excess welfare loss of

the consumers over the tax revenues collected by the government and can be interpreted as the hidden costs of …nancing public spending. A positive value for the marginal excess burden indicates a loss in welfare after the …scal reform.

We study here the welfare e¤ect of the …scal change for a generation during its life-cycle, once the …nal steady state equilibrium is reached. Let us determine the compensatory income variation which, after the balanced …scal reform (d¿w _{= ¤ d¿}e_{), would leave the level of}

life-cycle utility unchanged (dU = 0): (1_{¡ ¯)} dc y cy + ¯ dco co ¡ ¯ ° d¦ ¦ = 0

We use the …rst-order conditions of the representative household’s pro-gram (3) and the de…nition of the compensatory income variation dRc:

dRc¡ ( ¹w¡ b) du = cy¤dpy+ py dcy+ co¤ dpo+ po dco

this leads to:

py dcy+ po dco_{¡ p}oco¤ °d¦ ¦¤ = 0

As usual in this literature (Bovenberg and de Mooij 1994), one can distinguish an environmental component dRe

c ³ dRe c = poco¤°d¦¦¤ ´ and a non-environmental one dRne c (dRnec = ( ¹w¡ b) du+cy¤dpy+co¤dpo): dRc= dRnec + dRec

The higher the increase in environmental welfare, the lower the increase in consumption prices and the wage decrease and the smaller will be the compensatory income variation.

4.1. The existence conditions of the first dividend (environmental dividend)

The variation of environmental welfare depends both on the sensitivity of welfare to pollution and on the sensitivity of pollution to the con-sumption of the two generations. As the environmental compensatory income variation grows with pollution, it is clear that the environ-mental welfare increases if and only if the pollution stock decreases. Di¤erentiating the expression for the steady-state pollution stock (13) yields:

h

a d¦ = dc

y _{+ dc}o

Where the consumption variations are given by the following expres-sions: - …rst-period consumption: dcy = ¤y_c d¿e with ¤y c = 0 @@cy @¿e ¡ + @c y @u ¡ @u @¿w + ¤ ? 1 A

If the increase of consumption tax results in an increase in labor tax (¤ > 0) the e¤ect concerning the consumption of the younger

individuals is unambiguously negative (unemployment increases since ¿w _{increases). At the contrary, in case of a cut in labor}

tax, consumption will decrease only if the negative e¤ect of the pollution tax is greater than the positive e¤ect allowed by the employment augmentation. - second-period consumption: dco= ¤o_c d¿e with ¤o_c = 0 @@co @¿e ¡ + 2 4@co @u ¡ @u @¿w + + @c o @r + @r @¿w ¡ 3 5_¤ ? 1 A

As for the …rst term (@co

@u @¿@uw), comments are quite similar to the

previous ones. The second one features the e¤ect of the tax on the interest rate. If the increase in ¿e _{requires an increase in ¿}w_,

both e¤ects of unemployment increasing and of consumption cost increasing diminish the second-period consumption co_{. If the}

in-crease in ¿e _{requires a cut in ¿}w_{, the e¤ect is unknown because}

the higher interest rate and the higher employment increase con-sumption while the higher environmental tax decreases it.

Finally, the variation of pollution is obtained by: h

a d¦ = (¤

y

c+ ¤oc) d¿e

Let us see the precise links between ¤, ¤y

c and ¤oc: - when ¤ < 0: 8 > < > : ¤y c < 0 if and only if @c y @u @¿@uw¤ <¡@c y @¿e ¤oc< 0 if and only if ³ @co @u @u @¿w +@c o @r @r @¿w ´ ¤ <¡@¿@coe

At each period of the household’s life, when the rise in pollution tax can be balanced through a reduction of the tax rate on labor, the …nal e¤ect on consumption will be negative if and only if the price e¤ect is greater than the unemployment e¤ect, that is if the consumption rise due to employment increase is more than compensated by the decrease due to price augmentation.

- when ¤ > 0: _½

¤y c < 0

¤oc< 0

The environmental dividend will be unambiguously obtained. Note that this will be the case if pollution tax is La¤er-e¢cient but the labor tax is La¤er-ine¢cient.

4.2. The existence conditions of a second dividend (efficiency dividend)

In this framework, the second dividend is obtained when the non-environmental compensatory income variation is negative (dRne

c < 0).

¡ welfare e¤ect through the unemployment rate: ( ¹w_{¡ b) du = ( ¹}w_{¡ b)} @u

@¿w ¤ d¿ e

As @u

@¿w > 0, but as the sign of ¤ is ambiguous, the e¤ect on

em-ployment is undetermined. If the pollution tax rise is balanced by an increase of the tax rate on labor, the employment will decrease, playing against the second dividend (the marginal excess burden would be higher);

¡ welfare e¤ects through price variations:

8 > > < > > : dpy₌ @py @¿e d¿e= a d¿e dpo= @p o @¿e d¿ e₊@po @r @r @¿w d¿ w ₌µ@po @¿e+ @po @r @r @¿w ¤ ¶ d¿e , 8 < : dpy_{= a d¿}e dpo= 1 1 + r µ a¡ po @r @¿w ¤ ¶ d¿e

The …rst-period consumption price increases unambiguously but the second-period price may diminish if ¤ < 0 (because @r

@¿w < 0).

In case of an increase of the tax rate on labor (¤ > 0), both prices are increasing which leads to rise the marginal excess burden of the …scal reform.

The …nal e¤ect on non-environmental welfare is measured by the compensatory income variation dRne

c : dRnec = ( ¹w¡ b) du + cy¤dpy + co¤dpo = · ( ¹w¡ b) _@¿@uw ¤ + a c y_{¤+ c}o_¤ 1 1 + r µ a¡ po _@¿@rw ¤ ¶¸ d¿e

Even in the more intuitive case of a decrease of the labor tax (¤ < 0) which might lead to an environmental dividend, the double dividend can not always be obtained. It depends on the relative magnitude of the e¤ects on the wage, on the environmental welfare and on the …scal base of the pollution tax.

but never associated with an employment dividend (because @u @¿w > 0)

nor an e¢ciency dividend . By contrast, when ¤ < 0; the employment dividend is warranted and, under some conditions, a double dividend according to Goulder’s de…nition (environmental and e¢ciency) can be obtained.

4.3. The existence conditions of a third dividend (intergenerational equity dividend)

Another important question can be asked: is there any possibility for the environmental reform not to imply any non-environmental welfare loss for the generations bearing it? In our static framework of a steady state, we can give a …rst and partial answer. Let us de…ne the com-pensatory income variation of the young generation dRy_{and of the old}

generation dRo _as: 8 > > > > > > > > < > > > > > > > > : dRy ₌ 2 4( ¹w¡ b) _@¿@u_w + ¤ ? +a c y¤ 3 5 d¿e dRo _{= dR}e c+ 2 4co¤ 1 1 + r 0 @a_{¡ p}o @r @¿w ¡ ¤ ? 1 A 3 5 d¿e

We de…ne our third dividend of intergenerational equity as the pos-sibility for both generations to be better o¤ after the …scal reform (dRy _{< 0 and dR}o_{< 0).}

If ¤ > 0, the young generation is harmed by the …scal reform, as well as the old one if the environmental dividend is too small relative to its non-environmental loss of welfare.

If ¤ < 0, the welfare gain of the old generation is not warranted: it will exist only if the environmental welfare increases enough to over-compensate the loss incurred because of the increasing pollution tax and the decreasing interest rate. More surprisingly, the compensatory income variation of the young can be negative if the unemployment decreases enough to overcompensate the loss of welfare induced by the taxation of their consumption. Because there is actually an employment dividend, the young generation can also bene…t from the environmental …scal reform: there is a third dividend, without any transfers between generations. To summarize, ¤ < 0 is the necessary condition, but not a su¢cient one, for the existence of a third dividend.

5. Conclusion

The recent literature on the double dividend issue leads to some clear results (Bosello, Carraro and Galeotti 2001): when the economy is made of one productive sector, using only one productive factor (labor), and one representative consumer, the strong version of the double dividend is rejected. Instead, when there are several productive factors and/or several consumer groups, the double dividend can be obtained but at the expense of equity (Bovenberg and van der Ploeg 1995, Proost and van Regemorter 1995, Bovenberg and Heijdra 1998). This property might question the relevance of the …scal reform if it harms some generations. Nevertheless, any environmental tax is based on the equity and intergenerational solidarity principle: it aims to give to the future generations the same environmental amenities as to the present gener-ations. But such a …scal reform will only be acceptable if it improves the global welfare of all generations, the present like the future ones.

We show that the …scal change does not always harm the welfare of the younger generation and, under certain assumptions about agents’ preferences, it is possible to obtain both a double dividend and the respect of intergenerational equity. If the …scal reform involves a rise in the labor tax rate, the environmental dividend will always be obtained but neither the second dividend (either employment or e¢ciency) nor the third dividend (equity) can be obtained. By contrast, if the en-vironmental enforcement of the …scal system yields a decrease of the labor tax rate, the environmental dividend is more likely to occur but the second and third dividends are less likely to occur that the fall in unemployment and the rise in interest rate are greater.

Acknowledgement

The authors would like to thank two anonymous referees for helpful comments.

Notes

1. ut can also be viewed as the unemployment duration within the

working life of each agent (normalized to 1). Granier and Michel (1994) show that, under perfect expectations, with homothetic util-ity function, this model is equivalent to any model where utwould

stand for the unemployment rate of the aggregate population. 2. Had we assumed that the younger are sensitive, but less sensitive,

to the pollution, the results of our model would be qualitatively the same.

3. Because of the logarithmic utility function, optimal consumption of the young and optimal saving do not depend on the interest rate. 4. It would be equivalent to consider a small open economy with

perfect capital mobility, where the interest rate would be imposed by the external world and thus would …x the real wage (including labor tax), causing therefore unemployment.

5. Note that dk

dA> 0; d¿dAw < 0; _d¿dkw < 0; _d¿duw > 0:

6. The unemployment bene…ts are supposed here to be invariant. The case of their indexation to the consumption price index would also have been interesting to consider (but more di¢cult to analytically deal with). Our assumption encompasses the case where the unem-ployment bene…t would be determined by a constant replacement rate (bt= bwt) because here the wage is …xed.

7. A tax is La¤er-e¢cient if its …scal revenue grows when the tax rate increases.

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